三种非线性弹性地基梁的变形和内力研究

Deformation and Internal Force Analysis of Three Kinds of Beams on Non-Linear Elastic Foundation

研究地基反力与地基梁挠度成非线性关系对长、中、短3种类型地基梁的变形和内力的影响。基于实验数据,分别将地基反力与梁的挠度拟合成线性关系和三次多项式关系;然后采用有限差分法和牛顿迭代法编程,解出非线性弹性地基梁和经典线弹性地基梁的挠度、转角、剪力和弯矩随地基梁长度变化的曲线。算例计算表明：对于短梁,非线性弹性地基梁和经典线弹性Winkler地基梁的变形和内力一致;对于中、长梁,二者的相对误差可达到10%～20%,因此在实际工程中应尽量考虑地基反力与沉降的非线性关系;中等长度非线性弹性地基梁和线弹性地基梁变形和内力的相对误差随梁长度变化而变化,而对于长的地基梁二者的相对误差不随梁长度改变而变化。

To study the influence of non-linear relationship of foundation reaction force and beam deflection on deformation and internal force of long, medium and short these three kinds of foundation beam. Based on experimental data, the reaction force of foundation and the beam deflection were fitted as linear relationship and cubic polynomial, and then did program with finite difference method and Newton iteration method, to solve the curve of beams＇ length and deflection, slope, shearing force, bending moment of non-linear elastic foundation beams and classical linear elastic foundation beams. The numerical ease showed the deformation and internal force of short non-linear and linear elastic Winkler beams are the same ; the relative errors could reach 10%-20% for medium and long beams, so the non-linear relationship of foundation reaction force and settlement should be considered in real engineering ; the relative error of the deformation and internal force of medium non-linear and linear elastic beams changed with the length of beams, but to long beams, the relative error did not changed with the length.